Which approach should I use to classify points above and below a sine function $y(x) = A + B \sin(Cx)$?
You can try using Fourier basis functions to transform your observable variables and then apply a general linear regression model. To clarify, if you have pairs of observables $(y_i, x_i)$ where $y_i$ is $i$-th output, and $x_i$ is $i$-th input then you can transform your input variable into vector
\begin{equation}
\phi = [1, \sin(x), \cos(x), \sin(2x), \cos(2x), \ldots, \sin(nx), \cos(nx)]
\end{equation}
where $n$ is some arbitrary number.
Then you will have a standard linear regression model
\begin{equation}
Y = A\Phi
\end{equation}
where $Y = [y_1, \ldots, y_n]$, $\Phi = [ \phi_1, \ldots, \phi_n]$ and $A$ is matrix of unknown parameters that you need to learn.